It is actually possible to have a notion of "before and after" without a notion of "how long". In the usual metric theory of spacetime, the metric provides both a causal structure and measure for spacetime separations. The causal structure tells you about before and after while the measure provides a sense of how far and how long. The usual Lorentz group preserves both these structures, but it is possible to take the causal structure as more fundamental. The transformations which preserve only the causal structure are called conformal transformations. These transformations keep the light cones of the theory invariant i.e. they preserve the path of light rays, and it these null lines that determine the causal structure. One is left with a spacetime that has an order given by the causal structure and a sense of nearness provided by the basic topology but no invariant metrical structure. It therefore makes sense to say that event A happened before event B, and that there is "something in between", but you can't measure the time between events.

Obviously our world is not conformally invariant, but this notion of conformal invariance actually has some physical applications. For example, it has bearing on the physics of particles at very high energy. It might also be relevant for understanding the origin of mass since a massless world would be conformally invariant. Also, in a certain technical sense the description of a relativistic string is conformally invariant.